Non-Linear Analysis of Axially Loaded Piles Using “t–z” and “q–z” Curves

  • E. G. PsaroudakisEmail author
  • G. E. Mylonakis
  • N. S. Klimis
State-of-the-Art Review


In the present work, the behaviour of a single pile submitted to axial loading is analyzed. Namely, we examine the static stiffness coefficient at the head of a flexible pile, vertically embedded in a homogeneous or multilayer soil of random geometry and mechanical properties. To solve the problem, an analytical closed form solution is developed, based on Winkler’s theory. The model is used in combination with suitable shape functions, which describe reliably the vertical movement of the pile with depth. By choosing the appropriate shape functions along with “t–z” and “q–z” curves and following an iterative process, a relatively accurate estimation of the vertical displacement at the head of the pile can be achieved. Unlike traditional numerical solutions, the proposed method does not require discretization of the pile into finite elements (and afterwards resolution of a system of linear equations of high order) but only discretization in sections aiming integration with depth.


Single pile Axial loading “t–z” and “q–z” curves Winkler’s theory 



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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Civil EngineeringDemocritus University of Thrace (DUTh)XanthiGreece
  2. 2.ThessalonikiGreece
  3. 3.Chair Geotechnics and Soil-Structure InteractionUniversity of BristolBristolUK
  4. 4.Section of Geotechnical Engineering, Department of Civil EngineeringDemocritus University of Thrace (DUTh)XanthiGreece

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